Question Number 1936 by 123456 last updated on 25/Oct/15 $${f}^{\mathrm{2}} \left({x}\right)−{f}\left({x}^{\mathrm{2}} \right)={a}\:\left[\mathrm{G}.\mathrm{Q1902}\right] \\ $$$${f}\left({x}\right)=? \\ $$ Commented by prakash jain last updated on 25/Oct/15 $$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{that}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{exists}\:\mathrm{except}…
Question Number 133004 by liberty last updated on 18/Feb/21 $$\mathrm{If}\:\int\:\frac{\mathrm{tan}\:\mathrm{x}}{\mathrm{1}+\mathrm{tan}\:\mathrm{x}+\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}}\:\mathrm{dx}\:=\:\mathrm{x}−\frac{{k}}{\:\sqrt{{A}}}\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{{k}\:\mathrm{tan}\:{x}+\mathrm{1}}{\:\sqrt{{A}}}\right)+\mathrm{C} \\ $$$$\mathrm{where}\:\mathrm{C}\:\mathrm{is}\:\mathrm{constant}\:\mathrm{of}\:\mathrm{integration}. \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{ordered}\:\mathrm{pair}\:\left({k},\mathrm{A}\right)\:\mathrm{is}\: \\ $$$$\mathrm{equal}\:\mathrm{to}\: \\ $$ Answered by EDWIN88 last updated…
Question Number 67471 by AnjanDey last updated on 27/Aug/19 $$\boldsymbol{{Evaluate}}:\int\sqrt{{x}\sqrt{{x}+\mathrm{1}}}\:{dx} \\ $$ Commented by MJS last updated on 28/Aug/19 $$\int\sqrt{{x}\sqrt{{x}+\mathrm{1}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{{x}}\:\rightarrow\:{dx}=\mathrm{2}\sqrt{{x}}{dt}\right] \\ $$$$=\mathrm{2}\int{t}^{\mathrm{2}} \left({t}^{\mathrm{2}}…
Question Number 133001 by Ahmed1hamouda last updated on 17/Feb/21 Commented by mr W last updated on 18/Feb/21 $$\infty \\ $$$${no}\:{closed}\:{volume}! \\ $$ Terms of Service…
Question Number 67466 by ~ À ® @ 237 ~ last updated on 27/Aug/19 $$ \\ $$$$ \\ $$$${let}\:{consider}\:\:\:{for}\:{all}\:{n}\geqslant\mathrm{1}\:{the}\:{real}\:\left({t}\right)_{{n}} \:={t}\left({t}+\mathrm{1}\right)…..\left({t}+{n}−\mathrm{1}\right) \\ $$$${Find}\:\:\:{L}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\left({t}\right)_{\mathrm{1}}…
Question Number 67467 by ~ À ® @ 237 ~ last updated on 27/Aug/19 $$ \\ $$$$ \\ $$$${Find}\:\:\:\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{\:{tlnt}}{\left(\mathrm{1}+{t}^{\mathrm{2}} \right)^{{x}} }\:{dt}\: \\ $$…
Question Number 1930 by Rasheed Soomro last updated on 24/Oct/15 $${f}\:'\left({x}\right)−{g}\left({x}\right)=\mathrm{0} \\ $$$${f}\left({x}\right)+{g}'\left({x}\right)=\mathrm{0} \\ $$$${f}\left({x}\right)=? \\ $$$${g}\left({x}\right)=? \\ $$ Answered by prakash jain last updated…
Question Number 67464 by lalitchand last updated on 27/Aug/19 $$\mathrm{prove}\:\:\:\mathrm{Cos}\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)+\mathrm{Cos}\left(\frac{\mathrm{4}\pi}{\mathrm{7}}\right)+\mathrm{Cos}\left(\frac{\mathrm{8}\pi}{\mathrm{7}}\right)=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by mind is power last updated on 27/Aug/19 $${Z}^{\mathrm{7}} −\mathrm{1}=\mathrm{0} \\ $$$$\Rightarrow\left({z}−\mathrm{1}\right)\left(\mathrm{1}+{z}+{z}^{\mathrm{2}}…
Question Number 67465 by ~ À ® @ 237 ~ last updated on 27/Aug/19 $$ \\ $$$$ \\ $$$$\:\:{let}\:{consider}\:{a}\:{function}\:{g}\:{defined}\:{by}\:\:\:{g}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dx}}{\:\sqrt{\left(\mathrm{1}−{x}\right)\left(\mathrm{1}+{ax}\right)}}\:\: \\ $$$${Give}\:{the}\:{defined}\:{Domain}\:{of}\:{g}\:\:{and}\:{simplify}\:{g}. \\ $$…
Question Number 1928 by Yozzi last updated on 24/Oct/15 $${Prove}\:{that},\:{if}\:{p}>{q}>\mathrm{0}\:{and}\:{x}\geqslant\mathrm{0},\:{then} \\ $$$$\:\:\:\:\:\frac{\mathrm{1}}{{p}}\left(\frac{{x}^{{p}} }{{p}+\mathrm{1}}−\mathrm{1}\right)\geqslant\frac{\mathrm{1}}{{q}}\left(\frac{{x}^{{q}} }{{q}+\mathrm{1}}−\mathrm{1}\right).\: \\ $$ Commented by Rasheed Soomro last updated on 24/Oct/15 $${Prove}\:{that},\:{if}\:{p}>{q}>\mathrm{0}\:{and}\:{x}\geqslant\mathrm{0},\:{then}…